Problem Solving Chemistry: it makes sense! Chemistry  college  life is all about solving problems Chemistry: it makes sense! Develop a logical plan (series of steps) from your known to your unknowns http://www.geneseo.edu/~mcknight/

Problem Solving and Dimensional Analysis Many problems in chemistry involve using relationships to convert one unit of measurement to another Conversion factors are relationships between two units May be exact or measured Conversion factors generated from equivalence statements e.g., 1 inch = 2.54 cm can give or

Problem Solving and Dimensional Analysis Arrange conversion factors so given unit cancels Arrange conversion factor so given unit is on the bottom of the conversion factor May “string” conversion factors So we do not need to know direct relationships, as long as we can find steps that leads to the desired units (known  unknown)

“Must have a Plan” a conceptual plan is a visual outline that shows the strategic route required to solve a problem for unit conversion, the plan focuses on units and how to convert one to another for problems that require equations, the conceptual plan focuses on solving the equation to find an unknown value

Concept Plans and Conversion Factors Convert inches into centimeters Find relationship equivalence: 1 in = 2.54 cm Write concept plan in cm Change equivalence into conversion factors with starting units on the bottom

A Systematic Approach Sort the information from the problem identify the given quantity and unit, the quantity and unit you want to find, any relationships implied in the problem Design a strategy to solve the problem (roadmap) Concept plan sometimes may want to work backwards each step involves a conversion factor or equation Apply the steps in the concept plan check that units cancel properly multiply terms across the top and divide by each bottom term Check the answer double check the set-up to ensure the unit at the end is the one you wished to find check to see that the size of the number is reasonable since centimeters are smaller than inches, converting inches to centimeters should result in a larger number

Example: Convert 1.76 yd. to centimeters Sort information Given: Find: 1.76 yd length, cm Strategize Concept Plan: Relationship 1.094 yd = 1 m 1 m = 100 cm yd m cm Follow the concept plan to solve the problem Solution: Sig. figs. and round Round: 160.8775 cm = 161 cm Check Check: Units & magnitude are correct

Practice – Convert 30.0 mL to quarts (1 L = 1.057 qt) (Hint: 1000 mL makes 1 L)

Units & magnitude are correct Convert 30.0 mL to quarts Sort information Given: Find: 30.0 mL volume, qts Strategize Concept Plan: Relationship: 1 L = 1.057 qt 1 L = 1000 mL mL L qt Follow the plan to solve the problem Solution: Sig. figs. and round Round: 0.03171 qt = 0.0317 qt Check Check: Units & magnitude are correct

Problem Solving with Equations When solving a problem using an equation, you are usually given all the variables except the one you want to find Solve the equation for the variable you wish to find, then substitute and compute

Using Density in Calculations Concept Plans: m, V D m, D V V, D m

Density Calculations We can use density as a conversion factor between mass and volume!! density of H2O = 1.0 g/mL \ 1.0 g H2O = 1 mL H2O density of Pb = 11.3 g/cm3 \ 11.3 g Pb = 1 cm3 Pb How much does 4.0 cm3 of lead weigh? = 4.0 cm3 Pb 11.3 g Pb 1 cm3 Pb 45 g Pb x

Question: The mass of fuel in a jet must be calculated before each flight to ensure that the jet is not too heavy. A 747 jet is fueled with 173,231 L of jet fuel. If the density of the fuel is 0.738 g/mL, what is the mass of the fuel in kilograms?

Units & magnitude are correct Example: What is the mass in kg of 173,231 L of jet fuel whose density is 0.738 g/mL? Sort information Given: Find: 173,231 L density = 0.738 g/mL mass, kg Strategize Concept Plan: Relationship 1 mL = 0.738 g, 1 mL = 10-3 L 1 kg = 1000 g L mL g kg Follow the concept plan to solve the problem Solution: Sig. figs. and round Round: 1.3 x 105 kg Check Check: Units & magnitude are correct

Counting Atoms by Moles If we can find the mass of a particular number of atoms, we can use this information to convert the mass of an element sample into the number of atoms in the sample. The number of atoms we use is 6.022 x 1023 and we call this a mole 1 mole = 6.022 x 1023 entities Like 1 dozen = 12 entities Avogadro’s Number

Example: Calculate the number of atoms in 2.45 mol of copper Given: Find: 2.45 mol Cu atoms Cu Concept Plan: 1 mol = 6.022 x 1023 atoms mol Cu atoms Cu Solution: Check: since the number is slightly greater than twice Avogadro’s number, it make sense

Relationship Between Moles and Mass The mass of one mole of atoms is called the molar mass The molar mass of an element, in grams, is numerically equal to the element’s atomic mass, in amu The lighter the atom, the less a mole weighs The lighter the atom, the more atoms there are in 1 g

Mole and Mass Relationships sulfur 32.06 g 1 mole carbon 12.01 g

Example: Calculate the # moles of carbon in 0.0265 g of pencil “lead” Given: Find: 0.0265 g C mol C Concept Plan: 1 mol C = 12.01 g g C mol C Solution: Check: since the given amount is much less than 1 mol C, the number makes sense

Example: How many copper atoms are in a copper penny weighing 3.10 g? Given: Find: 3.10 g Cu atoms Cu Concept Plan: 1 mol Cu = 63.55 g, 1 mol = 6.022 x 1023 g Cu mol Cu atoms Cu Solution: Check: since the given amount is much less than 1 mol Cu, the number makes sense